From what I heard she was bucked off. I imagine she was doing the "gallop through the countryside" thing. Very British. Very stupid for a new rider.
I try to look at all the really bad accidents and have concluded that most that I hear about seem to happen outside the arena, on trails. I try to stay in the arena (which is easier being an English rider) and always anticipate that my horse can spook, stop short or do any number of things that can cause me to be "ejected." I try to look at every ride from the point of view of the horse. Why would they want to have me on them? It's a hot day, they'd rather eat, stand around whatever. I mention this because when you get really in tune with your horse you're less likely to get thrown because you're anticipating what's going on from their perspective. It's not always as free spirited a ride but it's a darn site better than ending up like Christopher Reeves.
Anyway, I thought I'd share that because anyone who has any tips to avert a tragedy might want to share them. I also have seen many videos of Christopher Reeve's riding and I'm sorry to say he was a terrible rider. He was very stiff and you could tell that if he fell he was going to hit like a rock. Always check your reins and stirrups. Be aware of the reins in your hands and keep your stirrups on the balls of your feet so that if you have to you can quickly dismount.
I just thought I'd share my observations because as you get older, the more aware you are of what can happen &, hopefully, the less likely you are to become a statistic. JMH2cents.
I think it's because they want to "muscle" their way into a correct form, they think they can achieve position by main force. Especially somebody as muscular as Reeve. If they stick with it, they realize that they have to relax and be soft and still and deep in the saddle. But I think it's harder for guys to do that.
I found a short clip of Reeve riding a crossrail on BBC and he didn't look that bad though.